Her great-grandfather served 23 years in the army in India before becoming a policeman, and her great-grandmother had to flee from the Indian Rebellion of 1857 after her father was killed.

[citation needed] Quick is perhaps best known for the role of Lady Julia Flyte in the television production of Brideshead Revisited.

She made her stage debut in A Midsummer Night's Dream at the Open Air Theatre, Regent's Park, London, in 1959.

Quick had played the same character as a younger woman in Alan Bennett's stageplay A Question of Attribution, one half of his Single Spies double bill.

[citation needed] From 1982 until 2008 her partner was English actor Bill Nighy with whom she worked in David Hare's A Map of the World at the National Theatre in 1982.

Quick was one of several celebrities who endorsed the successful parliamentary candidacy of the Green Party's Caroline Lucas at the 2015 general election.